Radiation pyrometers are known and commercially available. Typically, pyrometers are used to optically measure the temperature of an object or “target.” Pyrometers are particularly useful when the target is difficult to measure via conductive means (e.g., a thermocouple) because the target is very hot or very delicate, contacting the target could affect the temperature measurement, or because the target is difficult to access due to the hostility of the environment.
Pyrometers tend to be of two types: brightness or ratio devices. Brightness and ratio pyrometers both utilize a solution of a form of the Planck Radiation Equation to calculate the target's measured temperature. The Planck Radiation Equation for spectral radiation emitted from an ideal blackbody is:
                              L          ⁡                      (            λ            )                          =                                                            2                ⁢                                                                  ⁢                                  hc                  2                                                            λ                5                                      [                                          ⅇ                                  hc                                      λ                    ⁢                                                                                  ⁢                                          k                      B                                        ⁢                    T                                                              -              1                        ]                                -            1                                              (                  Equation          ⁢                                          ⁢          1                )            
where L(λ)=radiance in energy per unit area per unit time per steradian per unit wavelength interval, and where
h=Plank's constant,
c=the speed of light,
λ=the wavelength of the radiation,
kB=Boltzman's constant, and
T=the absolute temperature.
For non-blackbodies, the radiance L(λ) can be modified by emissivity ε to give a radiance as follows:
                              H          ⁡                      (            λ            )                          =                              ε            ⁢                                                  ⁢                          L              ⁡                              (                λ                )                                              =                      ε            ⁢                                                                                2                    ⁢                                                                                  ⁢                                          hc                      2                                                                            λ                    5                                                  [                                                      ⅇ                                          hc                                              λ                        ⁢                                                                                                  ⁢                                                  k                          B                                                ⁢                        T                                                                              -                  1                                ]                                            -                1                                                                        (                  Equation          ⁢                                          ⁢          2                )            
Equation 2 can be rewritten in terms of photocurrent to derive Equation 3, which describes the photocurrent detected by a pyrometer:
                              P          ⁡                      (            λ            )                          =                                                                              c                  1                                ⁢                ε                ⁢                                                                  ⁢                α                                            λ                5                                      ⁡                          [                                                ⅇ                                                            c                      2                                                                                      λ                        ⁢                                                                                                  ⁢                        T                                            ⁢                                                                                                                                          -                1                            ]                                            -            1                                              (                  Equation          ⁢                                          ⁢          3                )            
Where C1 is a constant equal to 2/π*h*c2, which is 3.74177*10−16 W/m2, and C2 is a constant equal to
      hc          k      B        .The variable α represents a sensor factor multiplied by a view factor, where the sensor factor represents a calibration of the pyrometer (e.g., the percentage of light that passes through optics of the pyrometer and/or optics of a view window of a processing chamber), and the view factor represents a percentage of all radiation from a source that is incident on a particular angular area. In other words, α is a variable that accounts for various factors that affect a ratio of the intensity of blackbody radiation emitted by an object divided by the intensity of blackbody radiation detected by the pyrometer (assuming blackbody-to-pyrometer radiation without reflections).
In the brightness method of pyrometry, H(λ) and ε are measured at a known wavelength, λ, and, therefore, T can be calculated. Brightness devices rely upon capturing a known fraction of the radiation from a source in a particular solid angle. Brightness pyrometers tend to depend on knowing the emissivity of the target, as required by Equation 3, supra. Emissivity ε is the ratio of the radiation emitted by the target to the radiation emitted by a perfect blackbody radiator at the same temperature. Typically, emissivity is unknown or estimated to a low degree of accuracy. Additionally, the emissivity is often a function of the target temperature, wavelength of radiation examined, and history of the target. These factors greatly limit the utility of brightness pyrometry. For repetitive processing of uniformly prepared and controlled substrates, such as polished silicon wafers, this limit of repeatable temperature measurement is relieved somewhat.
In practice, it is left to the user of a brightness pyrometer to estimate the target emissivity, usually based upon an analysis of the target's composition. The target's thermal and environmental history can alter the emissivity to an unkown degree, as well as current environmental factors such as gases that absorb certain wavelengths of radiation en route from the target to the pyrometer.
Ratio pyrometers depend upon graybody behavior. A graybody is an energy radiator which has a blackbody energy distribution, times an emissivity, throughout a wavelength interval being examined. Ratio pyrometers detect the radiation intensity at two known wavelengths and, utilizing Planck's Equation, calculate a temperature that correlates to the radiation intensity at the two specified wavelengths.